A332678 Decimal expansion of (1/2) * (1 + 2/1 + 4/(2*1) + 8/(4*2*1) + ... ).

3, 1, 4, 1, 6, 3, 2, 5, 6, 0, 6, 5, 5, 1, 5, 3, 8, 6, 6, 2, 9, 3, 8, 4, 2, 7, 7, 0, 2, 2, 5, 4, 2, 9, 4, 3, 4, 2, 2, 6, 0, 6, 1, 5, 3, 7, 9, 5, 6, 7, 3, 9, 7, 4, 7, 8, 0, 4, 6, 5, 1, 6, 2, 2, 3, 8, 0, 1, 4, 4, 6, 0, 3, 7, 3, 3, 3, 5, 1, 7, 7, 5, 6, 0, 0, 3, 6, 4, 1, 7, 1, 6, 2, 3, 3, 5, 9, 1, 3, 3, 0, 8, 6

Offset

1,1

Comments

An approximation to Pi.

Links

Table of n, a(n) for n=1..103.

Formula

Equals (1/2)*Sum_{k>=0} 2^(k-binomial(k,2)). - Andrew Howroyd, Feb 21 2020

Equals A190405 +2.5 = A299998 +1.5. All digits the same but the first one or two. - R. J. Mathar, Mar 10 2020

Example

3.1416325606551538662938427702254294342260615379567...

Maple

c:= sum(2^(j*(3-j)/2-1), j=0..infinity):
evalf(c, 125);  # Alois P. Heinz, Mar 03 2020

Prog

(PARI) suminf(k=0, 2^(k-binomial(k, 2)-1)) \\ Andrew Howroyd, Feb 21 2020

Crossrefs

Cf. A000796 (Pi), A013705.

Sequence in context: A014462 A309992 A016474 * A069264 A347459 A064575

Adjacent sequences: A332675 A332676 A332677 * A332679 A332680 A332681

Keyword

nonn,cons

Author

Drew Edgette, Feb 19 2020

Status

approved